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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.transform;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.FunctionUtils;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.complex.Complex;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.27"></a>
<FONT color="green">028</FONT>    <a name="line.28"></a>
<FONT color="green">029</FONT>    /**<a name="line.29"></a>
<FONT color="green">030</FONT>     * Implements the Fast Cosine Transform for transformation of one-dimensional<a name="line.30"></a>
<FONT color="green">031</FONT>     * real data sets. For reference, see James S. Walker, &lt;em&gt;Fast Fourier<a name="line.31"></a>
<FONT color="green">032</FONT>     * Transforms&lt;/em&gt;, chapter 3 (ISBN 0849371635).<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * There are several variants of the discrete cosine transform. The present<a name="line.34"></a>
<FONT color="green">035</FONT>     * implementation corresponds to DCT-I, with various normalization conventions,<a name="line.35"></a>
<FONT color="green">036</FONT>     * which are specified by the parameter {@link DctNormalization}.<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * DCT-I is equivalent to DFT of an &lt;em&gt;even extension&lt;/em&gt; of the data series.<a name="line.38"></a>
<FONT color="green">039</FONT>     * More precisely, if x&lt;sub&gt;0&lt;/sub&gt;, &amp;hellip;, x&lt;sub&gt;N-1&lt;/sub&gt; is the data set<a name="line.39"></a>
<FONT color="green">040</FONT>     * to be cosine transformed, the extended data set<a name="line.40"></a>
<FONT color="green">041</FONT>     * x&lt;sub&gt;0&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt;, &amp;hellip;, x&lt;sub&gt;2N-3&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt;<a name="line.41"></a>
<FONT color="green">042</FONT>     * is defined as follows<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;ul&gt;<a name="line.43"></a>
<FONT color="green">044</FONT>     * &lt;li&gt;x&lt;sub&gt;k&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt; = x&lt;sub&gt;k&lt;/sub&gt; if 0 &amp;le; k &amp;lt; N,&lt;/li&gt;<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;li&gt;x&lt;sub&gt;k&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt; = x&lt;sub&gt;2N-2-k&lt;/sub&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * if N &amp;le; k &amp;lt; 2N - 2.&lt;/li&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * &lt;/ul&gt;<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;p&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * Then, the standard DCT-I y&lt;sub&gt;0&lt;/sub&gt;, &amp;hellip;, y&lt;sub&gt;N-1&lt;/sub&gt; of the real<a name="line.49"></a>
<FONT color="green">050</FONT>     * data set x&lt;sub&gt;0&lt;/sub&gt;, &amp;hellip;, x&lt;sub&gt;N-1&lt;/sub&gt; is equal to &lt;em&gt;half&lt;/em&gt;<a name="line.50"></a>
<FONT color="green">051</FONT>     * of the N first elements of the DFT of the extended data set<a name="line.51"></a>
<FONT color="green">052</FONT>     * x&lt;sub&gt;0&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt;, &amp;hellip;, x&lt;sub&gt;2N-3&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt;<a name="line.52"></a>
<FONT color="green">053</FONT>     * &lt;br/&gt;<a name="line.53"></a>
<FONT color="green">054</FONT>     * y&lt;sub&gt;n&lt;/sub&gt; = (1 / 2) &amp;sum;&lt;sub&gt;k=0&lt;/sub&gt;&lt;sup&gt;2N-3&lt;/sup&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     * x&lt;sub&gt;k&lt;/sub&gt;&lt;sup&gt;&amp;#35;&lt;/sup&gt; exp[-2&amp;pi;i nk / (2N - 2)]<a name="line.55"></a>
<FONT color="green">056</FONT>     * &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;k = 0, &amp;hellip;, N-1.<a name="line.56"></a>
<FONT color="green">057</FONT>     * &lt;p&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * The present implementation of the discrete cosine transform as a fast cosine<a name="line.58"></a>
<FONT color="green">059</FONT>     * transform requires the length of the data set to be a power of two plus one<a name="line.59"></a>
<FONT color="green">060</FONT>     * (N&amp;nbsp;=&amp;nbsp;2&lt;sup&gt;n&lt;/sup&gt;&amp;nbsp;+&amp;nbsp;1). Besides, it implicitly assumes<a name="line.60"></a>
<FONT color="green">061</FONT>     * that the sampled function is even.<a name="line.61"></a>
<FONT color="green">062</FONT>     *<a name="line.62"></a>
<FONT color="green">063</FONT>     * @version $Id: FastCosineTransformer.java 1385310 2012-09-16 16:32:10Z tn $<a name="line.63"></a>
<FONT color="green">064</FONT>     * @since 1.2<a name="line.64"></a>
<FONT color="green">065</FONT>     */<a name="line.65"></a>
<FONT color="green">066</FONT>    public class FastCosineTransformer implements RealTransformer, Serializable {<a name="line.66"></a>
<FONT color="green">067</FONT>    <a name="line.67"></a>
<FONT color="green">068</FONT>        /** Serializable version identifier. */<a name="line.68"></a>
<FONT color="green">069</FONT>        static final long serialVersionUID = 20120212L;<a name="line.69"></a>
<FONT color="green">070</FONT>    <a name="line.70"></a>
<FONT color="green">071</FONT>        /** The type of DCT to be performed. */<a name="line.71"></a>
<FONT color="green">072</FONT>        private final DctNormalization normalization;<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>        /**<a name="line.74"></a>
<FONT color="green">075</FONT>         * Creates a new instance of this class, with various normalization<a name="line.75"></a>
<FONT color="green">076</FONT>         * conventions.<a name="line.76"></a>
<FONT color="green">077</FONT>         *<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param normalization the type of normalization to be applied to the<a name="line.78"></a>
<FONT color="green">079</FONT>         * transformed data<a name="line.79"></a>
<FONT color="green">080</FONT>         */<a name="line.80"></a>
<FONT color="green">081</FONT>        public FastCosineTransformer(final DctNormalization normalization) {<a name="line.81"></a>
<FONT color="green">082</FONT>            this.normalization = normalization;<a name="line.82"></a>
<FONT color="green">083</FONT>        }<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>        /**<a name="line.85"></a>
<FONT color="green">086</FONT>         * {@inheritDoc}<a name="line.86"></a>
<FONT color="green">087</FONT>         *<a name="line.87"></a>
<FONT color="green">088</FONT>         * @throws MathIllegalArgumentException if the length of the data array is<a name="line.88"></a>
<FONT color="green">089</FONT>         * not a power of two plus one<a name="line.89"></a>
<FONT color="green">090</FONT>         */<a name="line.90"></a>
<FONT color="green">091</FONT>        public double[] transform(final double[] f, final TransformType type)<a name="line.91"></a>
<FONT color="green">092</FONT>          throws MathIllegalArgumentException {<a name="line.92"></a>
<FONT color="green">093</FONT>            if (type == TransformType.FORWARD) {<a name="line.93"></a>
<FONT color="green">094</FONT>                if (normalization == DctNormalization.ORTHOGONAL_DCT_I) {<a name="line.94"></a>
<FONT color="green">095</FONT>                    final double s = FastMath.sqrt(2.0 / (f.length - 1));<a name="line.95"></a>
<FONT color="green">096</FONT>                    return TransformUtils.scaleArray(fct(f), s);<a name="line.96"></a>
<FONT color="green">097</FONT>                }<a name="line.97"></a>
<FONT color="green">098</FONT>                return fct(f);<a name="line.98"></a>
<FONT color="green">099</FONT>            }<a name="line.99"></a>
<FONT color="green">100</FONT>            final double s2 = 2.0 / (f.length - 1);<a name="line.100"></a>
<FONT color="green">101</FONT>            final double s1;<a name="line.101"></a>
<FONT color="green">102</FONT>            if (normalization == DctNormalization.ORTHOGONAL_DCT_I) {<a name="line.102"></a>
<FONT color="green">103</FONT>                s1 = FastMath.sqrt(s2);<a name="line.103"></a>
<FONT color="green">104</FONT>            } else {<a name="line.104"></a>
<FONT color="green">105</FONT>                s1 = s2;<a name="line.105"></a>
<FONT color="green">106</FONT>            }<a name="line.106"></a>
<FONT color="green">107</FONT>            return TransformUtils.scaleArray(fct(f), s1);<a name="line.107"></a>
<FONT color="green">108</FONT>        }<a name="line.108"></a>
<FONT color="green">109</FONT>    <a name="line.109"></a>
<FONT color="green">110</FONT>        /**<a name="line.110"></a>
<FONT color="green">111</FONT>         * {@inheritDoc}<a name="line.111"></a>
<FONT color="green">112</FONT>         *<a name="line.112"></a>
<FONT color="green">113</FONT>         * @throws org.apache.commons.math3.exception.NonMonotonicSequenceException<a name="line.113"></a>
<FONT color="green">114</FONT>         * if the lower bound is greater than, or equal to the upper bound<a name="line.114"></a>
<FONT color="green">115</FONT>         * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException<a name="line.115"></a>
<FONT color="green">116</FONT>         * if the number of sample points is negative<a name="line.116"></a>
<FONT color="green">117</FONT>         * @throws MathIllegalArgumentException if the number of sample points is<a name="line.117"></a>
<FONT color="green">118</FONT>         * not a power of two plus one<a name="line.118"></a>
<FONT color="green">119</FONT>         */<a name="line.119"></a>
<FONT color="green">120</FONT>        public double[] transform(final UnivariateFunction f,<a name="line.120"></a>
<FONT color="green">121</FONT>            final double min, final double max, final int n,<a name="line.121"></a>
<FONT color="green">122</FONT>            final TransformType type) throws MathIllegalArgumentException {<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>            final double[] data = FunctionUtils.sample(f, min, max, n);<a name="line.124"></a>
<FONT color="green">125</FONT>            return transform(data, type);<a name="line.125"></a>
<FONT color="green">126</FONT>        }<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>        /**<a name="line.128"></a>
<FONT color="green">129</FONT>         * Perform the FCT algorithm (including inverse).<a name="line.129"></a>
<FONT color="green">130</FONT>         *<a name="line.130"></a>
<FONT color="green">131</FONT>         * @param f the real data array to be transformed<a name="line.131"></a>
<FONT color="green">132</FONT>         * @return the real transformed array<a name="line.132"></a>
<FONT color="green">133</FONT>         * @throws MathIllegalArgumentException if the length of the data array is<a name="line.133"></a>
<FONT color="green">134</FONT>         * not a power of two plus one<a name="line.134"></a>
<FONT color="green">135</FONT>         */<a name="line.135"></a>
<FONT color="green">136</FONT>        protected double[] fct(double[] f)<a name="line.136"></a>
<FONT color="green">137</FONT>            throws MathIllegalArgumentException {<a name="line.137"></a>
<FONT color="green">138</FONT>    <a name="line.138"></a>
<FONT color="green">139</FONT>            final double[] transformed = new double[f.length];<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>            final int n = f.length - 1;<a name="line.141"></a>
<FONT color="green">142</FONT>            if (!ArithmeticUtils.isPowerOfTwo(n)) {<a name="line.142"></a>
<FONT color="green">143</FONT>                throw new MathIllegalArgumentException(<a name="line.143"></a>
<FONT color="green">144</FONT>                    LocalizedFormats.NOT_POWER_OF_TWO_PLUS_ONE,<a name="line.144"></a>
<FONT color="green">145</FONT>                    Integer.valueOf(f.length));<a name="line.145"></a>
<FONT color="green">146</FONT>            }<a name="line.146"></a>
<FONT color="green">147</FONT>            if (n == 1) {       // trivial case<a name="line.147"></a>
<FONT color="green">148</FONT>                transformed[0] = 0.5 * (f[0] + f[1]);<a name="line.148"></a>
<FONT color="green">149</FONT>                transformed[1] = 0.5 * (f[0] - f[1]);<a name="line.149"></a>
<FONT color="green">150</FONT>                return transformed;<a name="line.150"></a>
<FONT color="green">151</FONT>            }<a name="line.151"></a>
<FONT color="green">152</FONT>    <a name="line.152"></a>
<FONT color="green">153</FONT>            // construct a new array and perform FFT on it<a name="line.153"></a>
<FONT color="green">154</FONT>            final double[] x = new double[n];<a name="line.154"></a>
<FONT color="green">155</FONT>            x[0] = 0.5 * (f[0] + f[n]);<a name="line.155"></a>
<FONT color="green">156</FONT>            x[n &gt;&gt; 1] = f[n &gt;&gt; 1];<a name="line.156"></a>
<FONT color="green">157</FONT>            // temporary variable for transformed[1]<a name="line.157"></a>
<FONT color="green">158</FONT>            double t1 = 0.5 * (f[0] - f[n]);<a name="line.158"></a>
<FONT color="green">159</FONT>            for (int i = 1; i &lt; (n &gt;&gt; 1); i++) {<a name="line.159"></a>
<FONT color="green">160</FONT>                final double a = 0.5 * (f[i] + f[n - i]);<a name="line.160"></a>
<FONT color="green">161</FONT>                final double b = FastMath.sin(i * FastMath.PI / n) * (f[i] - f[n - i]);<a name="line.161"></a>
<FONT color="green">162</FONT>                final double c = FastMath.cos(i * FastMath.PI / n) * (f[i] - f[n - i]);<a name="line.162"></a>
<FONT color="green">163</FONT>                x[i] = a - b;<a name="line.163"></a>
<FONT color="green">164</FONT>                x[n - i] = a + b;<a name="line.164"></a>
<FONT color="green">165</FONT>                t1 += c;<a name="line.165"></a>
<FONT color="green">166</FONT>            }<a name="line.166"></a>
<FONT color="green">167</FONT>            FastFourierTransformer transformer;<a name="line.167"></a>
<FONT color="green">168</FONT>            transformer = new FastFourierTransformer(DftNormalization.STANDARD);<a name="line.168"></a>
<FONT color="green">169</FONT>            Complex[] y = transformer.transform(x, TransformType.FORWARD);<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>            // reconstruct the FCT result for the original array<a name="line.171"></a>
<FONT color="green">172</FONT>            transformed[0] = y[0].getReal();<a name="line.172"></a>
<FONT color="green">173</FONT>            transformed[1] = t1;<a name="line.173"></a>
<FONT color="green">174</FONT>            for (int i = 1; i &lt; (n &gt;&gt; 1); i++) {<a name="line.174"></a>
<FONT color="green">175</FONT>                transformed[2 * i]     = y[i].getReal();<a name="line.175"></a>
<FONT color="green">176</FONT>                transformed[2 * i + 1] = transformed[2 * i - 1] - y[i].getImaginary();<a name="line.176"></a>
<FONT color="green">177</FONT>            }<a name="line.177"></a>
<FONT color="green">178</FONT>            transformed[n] = y[n &gt;&gt; 1].getReal();<a name="line.178"></a>
<FONT color="green">179</FONT>    <a name="line.179"></a>
<FONT color="green">180</FONT>            return transformed;<a name="line.180"></a>
<FONT color="green">181</FONT>        }<a name="line.181"></a>
<FONT color="green">182</FONT>    }<a name="line.182"></a>




























































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